well, I know you're supposed to find the derivatives and use it to determine the max. value of the area, but I have no idea how. I've started out by doing:

dA
---= 40x-(x^2)
dx

after that, I'm lost

You have the right idea, but took your derivative wrong:

Now, what does the derivative of a function mean? It is the slope of the line tangent to the function at a given value of x. What happens to the derivative of a function when the function is at a relative maximum or minimum?